The curve above is the graph of a sinusoidal function. it goes through the points
(-6,0)and (4,0)(4,0). find a sinusoidal function that matches the given graph. if needed, you can enter π=3. as 'pi' in your answer, otherwise use at least 3 decimal digits.

  y = 4cos((π/5)x) +3

Step-by-step explanation:

The graph shows the peak of the function to be at x=0, so a cosine function is an appropriate choice for the model.

The value of A is half the difference between the minimum and maximum, so is ...

  A = (1/2)(7 -(-1)) = 4

The value of C is the average of the maximum and the minimum, so is ...

  C = (1/2)(7 +(-1)) = 3

The value of k must be chosen so that for one full period, kx is 2π. We note that one minimum is at -5, and the next is at +5, so the period of this waveform is (5 -(-5)) = 10. Then ...

  k·10 = 2π

  k = π/5 . . . . . divide by 10 and reduce the fraction

Now, we have all the parameters of our function:

  y = 4cos((π/5)x) +3

15

step-by-step explanation:

10

step-by-step explanation: